For efficient energy management of an electrical energy storage system comprising batteries or supercapacitors, an adaptive algorithm that can characterize the state of the energy-storage device is required. Inputs to the algorithm can include the system current, voltage, and temperature, and outputs characterize the energy content (i.e., state of charge, or ‘SOC’, predicted power capability (i.e., state of power, or ‘SOP’), and performance relative to the new and end-of-life condition (i.e., state of health, or ‘SOH’). For automotive applications, the conversion of input information to outputs for vehicle control must occur quickly, while not requiring substantial amounts of computer storage, consistent with embedded-controller and serial-data-transfer capabilities. Generally these two limitations mandate that algorithms be fully recursive, wherein all information utilized by the algorithm stems from previous time-step values and measurements that are immediately available.
To construct a state estimator for the SOC, SOH, and SOP, model reference adaptive systems have been employed. In a typical approach, a model of the plant, e.g., a battery, is constructed, and the parameters appearing in the model are regressed from the available measurements. For example, using an equivalent circuit as depicted with reference to FIG. 1, a mathematical expression may be constructed for the battery, and the values of the circuit elements can be regressed from the available current, voltage, and temperature data during ongoing vehicle operation. One method of using weighted recursive least squares (‘WRLS’) with exponential forgetting has proven to be a pragmatic approach for parameter regression, when model reference adaptive systems are employed. The time-weighting of data is damped exponentially with this approach; hence, new data has a preferential impact in determining the value of regressed parameters and thus the state of the system.
Two shortfalls arise in a standard implementation of WRLS. First, a single forgetting factor is typically employed for all parameters, even where different parameters may have significantly different temporal considerations. Secondly, the value of the forgetting factors cannot be optimized for each parameter, due to use of a single, common factor. The result of such implementation of WRLS is a state estimator for state of charge (SOC), state of health (SOH), and state of power (SOP) of a battery or other system that lacks accuracy and reliability due to such compromises.
Therefore, what is needed is a state estimator for SOC, SOH, and SOP that is able to provide a more accurate prediction of those values. This need for a more accurate state estimator for state of charge is important, for example, on modern vehicle systems with highly efficient battery control for an electric vehicle, or, for control of a hybrid electric vehicle.